What are the solutions to the equation 6x^{(3)}+9x^{(2)}+4x+6=0 ?

The solutions to the equation 6x^{(3)}+9x^{(2)}+4x+6=0 are x=-3/2 ,x=sqrt(2/3)i,x=-sqrt(2/3)i

Find the zeros of 6x^{(3)}+9x^{(2)}+4x+6=0

The zeros of 6x^{(3)}+9x^{(2)}+4x+6=0 are x=-3/2 ,x=sqrt(2/3)i,x=-sqrt(2/3)i

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6 x^{(3)} + 9 x^{(2)} + 4 x + 6 = 0

x = - \frac{3}{2}, x = \frac{2}{3} i, x = - \frac{2}{3} i

Solution steps

6 x^{(3)} + 9 x^{(2)} + 4 x + 6 = 0

Refine

6 x^{3} + 9 x^{2} + 4 x + 6 = 0

Factor

6 x^{3} + 9 x^{2} + 4 x + 6 : (2 x + 3) (3 x^{2} + 2)

(2 x + 3) (3 x^{2} + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x + 3 = 0 or 3 x^{2} + 2 = 0

Solve

2 x + 3 = 0 : x = - \frac{3}{2}

Solve

3 x^{2} + 2 = 0 : x = \frac{2}{3} i, x = - \frac{2}{3} i

The solutions are

x = - \frac{3}{2}, x = \frac{2}{3} i, x = - \frac{2}{3} i

405 = 5 x^{3}

x^{3} + 5 x^{2} + 16 x + 80 = 0

0 = x^{4} - 4 x^{2} - 45

(1 - y) (3 - y) (6 - y) = - 70

(x - 5)^{3} - 2 = 5^{2}

What are the solutions to the equation 6x^{(3)}+9x^{(2)}+4x+6=0 ?
The solutions to the equation 6x^{(3)}+9x^{(2)}+4x+6=0 are x=-3/2 ,x=sqrt(2/3)i,x=-sqrt(2/3)i
Find the zeros of 6x^{(3)}+9x^{(2)}+4x+6=0
The zeros of 6x^{(3)}+9x^{(2)}+4x+6=0 are x=-3/2 ,x=sqrt(2/3)i,x=-sqrt(2/3)i